1. Technical Field
The present invention pertains to communication systems. In particular, the present invention pertains to acquisition of pseudonoise codes or carrier signals during conditions of relatively large chip rate uncertainty. The present invention is typically applied to Direct Sequence Spread Spectrum systems, where waveforms are employed in the form of coded spread spectrum signals and the signals are expanded in bandwidth via a pseudonoise or spreading code.
2. Discussion of Related Art
Generally, wireless communication systems employ a carrier signal to transport information between sites. Information is basically modulated onto the carrier signal for transmission. A conventional modulating technique employed by communication systems is Binary Phase Shift Keying (BPSK). This technique basically shifts the phase of a signal based on the value of a digital bit stream. For example, a logical one value in the bit stream causes the signal to be shifted in phase, while no phase shift is produced in response to a logical zero value in the bit stream (e.g., this is commonly referred to as an NRZ type scheme).
A receiver receives a signal from the environment and attempts to acquire or determine the presence of the carrier signal within the received signal. Once the carrier signal is acquired, the information transported by the carrier signal may be retrieved. A conventional architecture employed for carrier acquisition of a modulated, non-spread signal is illustrated in FIG. 1. In particular, a received bandpass signal, Sbp(t), is combined with white noise, w(t), having a power spectral density of N0 via a summer 10. The bandpass signal is basically a form of the input signal received by the receiver from the environment. This signal is a function of the received carrier signal frequency and may be expressed as follows:Sbp(t)=x(t)[cos(2πfrt)−sin(2πfrt)],where fr is the received carrier frequency and x(t) is a random binary wave (e.g., a random sequence of binary symbols). The binary symbols have amplitude values of “+A” and “−A” (e.g., each amplitude value occurring with equal probability), and a duration of 1/Rs seconds, where Rs is the signaling rate. For uncoded signals, the signaling rate, Rs, typically equals the data rate, Dr. For rate one-half coded signals, the signaling rate is equal to twice the data rate (e.g., Rs=2Dr).
The combined signal from summer 10 is filtered by a bandpass filter 12. The bandpass filter generally produces portions of the combined signal within a desired frequency range, thereby removing spurious signal components. The filtered signal is applied to a mixer 14 that mixes the filtered signal with a local carrier signal, l(t). The local carrier signal may be expressed as follows:l(t)=ej2πflt where fl is the local carrier frequency.
The mixed signal from mixer 14 is applied to a low pass filter 16 to produce a baseband signal, Sbb(t). The lowpass filter basically serves to produce desired baseband signal components from the mixed signal. Since the local carrier signal frequency typically differs from the received carrier signal frequency, the resulting baseband signal is a function of the difference between those frequencies and may be expressed as follows:Sbb(t)=x(t)ej2πΔft+ni(t)+jnq(t),where Δf is the baseband carrier offset or the difference between the received carrier signal frequency, fr, and the local carrier signal frequency, fl (e.g., Δf=fr−fl). The variables ni(t) and nq(t) within the complex expression are independent gaussian random variables that serve as thermal noise components. Carrier acquisition basically attempts to measure the baseband carrier offset in order to determine the received carrier frequency.
The precise optimal sample rate for carrier acquisition depends on the sequence of binary symbols produced by the process x(t). Since this binary sequence is generally not known, the sampling rate, fs, for the NRZ symbol format described above may be set to twice the signaling or modulation rate (e.g., fs=2Rs). In the case of a bi-phase symbol format, the sampling rate, fs, may be set to four times the signaling rate (e.g., fs=4Rs). Increased rates of sampling are not practical due to the prohibitive squaring losses imposed by the data stripping function described below. Lower rates of sampling are similarly not practical due to signal cancellation or loss associated with data transitions in x(t), and the pulse shape with respect to bi-phase symbol formats.
The baseband signal is applied to a data stripping module 18. The data stripping module basically produces a phasor to enable measurement of the baseband carrier offset and performs the following function:Iout=2IinQin  (Equation 1)Qout=IinIin−QinQin  (Equation 2)where “I” and “Q” respectively indicate the In-phase and Quadrature (e.g., complex) signal components and the subscripts “in” and “out” respectively represent the input and output of the data stripping module. The spectrum of the input baseband signal to the data stripping module includes a sinc function in noise centered at the baseband carrier offset, Δf. The spectrum of the output signal from the data stripping module includes a spectral line (e.g., tone) in noise. The spectral location of this line is twice the baseband carrier offset, Δf. This is commonly referred to as the “frequency doubling effect”.
The output of the data stripping module is directed to an FFT and peak search module 20. This module basically measures the baseband carrier offset, Δf. In general, the one sided bandwidth of a complex Fast Fourier Transform (FFT) is one-half of the sampling rate (e.g., fs/2), while the resolution of the FFT is the sampling rate divided by the FFT size (e.g., fs/Nfft, where Nfft is the FFT size or quantity of stages (e.g., log base two of the number of points) within the FFT)). However, due to the frequency doubling of the output signal from the data stripping module, the one sided bandwidth of the FFT is effectively reduced to one-quarter of the sampling rate (e.g., fs/4), while the resolution is reduced by half (e.g., fs/(2Nfft)). If the absolute value of the baseband carrier offset is less than the one-sided bandwidth (e.g., |Δf|<fs/4), the Nyquist criteria is satisfied and the position of the maximum or peak value within the FFT output (e.g., the FFT basically produces an array of bins each associated with a magnitude, where the peak value is the largest magnitude within an array element or bin) corresponds to the baseband carrier offset, Δf (e.g., when the signal to noise ratio (SNR) is of a sufficiently high magnitude). When the absolute value of the baseband carrier offset is greater than the one-sided FFT bandwidth (e.g., |Δf|>fs/4), the Nyquist criteria is not satisfied and aliasing occurs. In this case, the peak value position within the FFT output generally does not correspond to the baseband carrier offset, Δf, and the measurement is corrupted.
In cases where the frequency uncertainty is large with respect to data rate (e.g., when the local carrier frequency, fl, may not be sufficiently close to the received carrier frequency, fr, to produce a baseband carrier offset of a sufficient magnitude to satisfy the Nyquist criteria), the carrier acquisition process must partition the frequency uncertainty region into discrete bands. These bands form a series of local carriers, li(t), spaced evenly in frequency throughout the entire frequency uncertainty region. Each local carrier, li(t), represents a frequency band, and an FFT and peak search is performed for each band. The center frequency for each band is the frequency of the band local carrier, fl(i). The bands in the series are processed sequentially, where the number of bands in the series is selected to ensure that at least one of the local carriers, li(t), is sufficiently close in frequency to the received carrier frequency, fr, to satisfy the Nyquist criteria (e.g., |fr−fl(i)|<fs/4).
The minimum number of bands required to guarantee that the Nyquist criteria will be satisfied for at least one local carrier, considering the one sided frequency uncertainty and the sample rate, may be expressed as follows:
                              N          B                =                              floor            ⁡                          (                              δ                                                      f                    s                                    /                  4                                            )                                +          1                                    (                  Equation          ⁢                                          ⁢          3                )            where NB is the number of bands, δ is the one sided frequency uncertainty, and fs is the sample rate.
The local carrier frequencies, fl(i), may be determined as follows based on the number of bands, NB, and the one sided frequency uncertainty, δ:
                                          f            l                    ⁡                      (            i            )                          =                                                                              2                  ⁢                                                                          ⁢                  δ                                                  N                  B                                            ⁡                              [                                  i                  -                                      (                                                                                            N                          B                                                -                        1                                            2                                        )                                                  ]                                      ⁢            0                    ≤          i          ≤                                    N              B                        -            1                                              (                  Equation          ⁢                                          ⁢          4                )            
The time interval to perform carrier acquisition in a particular band, Tcar—acq, may be expressed as follows:Tcar—acq=Tc+Tp  (Equation 5)where Tc is the time interval to collect the time domain data (e.g., Tc=Nfft/fs) and Tp is the time interval to process the time domain data (e.g., the time interval to compute the FFT, conduct the peak search, and render a decision). Accordingly, the carrier acquisition time is based on the sample rate, fs (e.g., which is based on the data rate and symbol format as described above), the size of the FFT, Nfft (e.g., which is based on the signal to noise ratio) and the processing time, Tp (e.g., which is based on processor speed and the size of the FFT, Nfft).
Signal to noise ratio (SNR) is inversely proportional to the minimum allowable carrier acquisition time. The size of the FFT, Nfft, is selected to be the minimum value that permits reliable detection of the signal. This is reflected mathematically by the following equation:SNRin−Lsq+Gfft>SNRdet  (Equation 6)where SNRin is the signal to noise ratio of the baseband signal at the input to the data stripping module, Lsq is the squaring loss associated with the data stripping function performed by the data stripping module, Gfft is the gain associated with averaging a signal in uncorrelated noise, and SNRdet is the minimum signal to noise ratio required to reliably detect the signal.
The signal to noise ratio at the data stripping module input, SNRin, is a function of data rate, symbol format, minimum energy per bit to noise density power ratio (Eb/No) and implementation loss. The squaring loss, Lsq, is solely a function of the signal to noise ratio at the data stripping module input, SNRin. The gain, Gfft, is a function of the size of the FFT, Nfft. A large sized FFT facilitates more averaging, thereby yielding greater signal to noise ratio gain. The minimum signal to noise ratio to reliably detect the signal, SNRdet, is a constant and determined based on the detection probability deemed to be “reliable”.
The size of the FFT, Nfft, is the only parameter adjustable by a designer for a particular user configuration to satisfy the above Equation 6. Accordingly, the designer determines the minimum size of the FFT (e.g., minimum value of Nfft) that satisfies the condition in above-described Equation 6. This value can then be inserted into above-described Equation 5 to determine the minimum allowable carrier acquisition time.
The signal processing operations and minimum time required to detect a signal reliably for carrier acquisition of a modulated, non-spread signal is described above. However, a manner of enhancing security and reliability within communication systems includes employment of encoded signals, such as spread spectrum signals. In particular, the operation of a Direct Sequence Spread Spectrum (DSSS) system includes spreading of a baseband signal (e.g., bandwidth expansion) by use of pseudonoise (PN) codes. The frequency rate of the codes greatly exceeds that of the baseband signal, where each transition or code symbol is commonly referred to as a “chip”. The codes or chips are basically modulated onto the baseband signal containing data and the resulting signal is mixed with an RF carrier signal and transmitted for reception by the appropriate receiving units. A cross correlation of an incoming signal with a suitable code replica by a digital matched filter (DMF) within the receiving unit produces an energy peak at the exact match, thereby rejecting or filtering other pseudonoise codes and background noise and interference.
Pseudonoise orthogonal or quasi-orthogonal codes may be selected to correlate exactly with a peak power output of the digital matched filter when the incoming signal code and replica codes match, and to produce a filter output of zero when these codes do not match (e.g., even if the codes are offset or shifted by one position). For example, an incoming signal including bi-phase modulated chips or codes is correlated with a stored replica code for a given time interval. Each chip within the incoming signal is multiplied by the corresponding chip in the replica code, where the individual products are summed to produce a correlation result. The filter operation may be expressed as:
      ∑          k      =      1        N    ⁢          ⁢            c      k        ⁢          r      k      where ck represents the incoming chip sequence, rk is the stored replica code and N represents the quantity of chips in the code. With respect to an exemplary incoming signal with a code of 1, 1, 1, −1, a correlation value of four is produced when this code is matched exactly to the stored replica code (e.g., the sum of the products of the corresponding chips, or (1×1)+(1×1)+(1×1)+(−1×−1)=4) indicating a peak power output of the filter. However, when an incoming signal with a code of 1, 1, −1, 1 does not match with a stored replica code of 1, 1, 1, −1, the filter provides a correlation value of zero (e.g., the sum of the products of the corresponding chips, or (1×1)+(1×1)+(−1×1)+(1×−1)=0) indicating the absence of a match.
The pseudonoise codes provide a manner for a receiving unit to basically identify and differentiate between messages directed to that unit and other units, and further ensures that other transmissions within the surrounding environment are not erroneously considered as messages addressed to the receiving unit. Moreover, the pseudonoise codes enable secure and reliable communications in the presence of background and/or multi-user interference, while the bandwidth expansion of the baseband signal distributes the signal power over a greater bandwidth, thereby reducing the power spectral density of that signal in maximum amplitude and reducing visibility of the signal in the environment.
The security provided by the pseudonoise codes is based on the requirement that the receivers have knowledge of the specific code being transmitted in order to acquire and demodulate the signal. Accordingly, long or lengthy pseudonoise codes are utilized in some commercial systems, where subsections of the code are used to spread symbols with subsequent symbols being spread by different subsections. This is typically employed by military systems having security as a key requirement.
Signal to Noise Ratio (SNR) is commonly defined as the ratio of the average signal power to the average noise power and is preferably measured in decibels. The average signal power is determined over the signal bandwidth, where the bandwidth for a spread spectrum signal is greater than that for a narrowband or baseband signal. For example, a baseband signal with 25 KHz of bandwidth and expanded at a ratio of one-hundred produces a spread signal with 25 KHz*100=2.5 MHz. The baseband signal includes, for a transmitted power of one Watt, a signal power of 1/25 KHz=0.040 Watts/Hz or 40 milliWatts/Hz, while the spread signal includes 1/2.5 MHz=400 NanoWatts/Hz. Thus, the spectral density of the narrowband or baseband signal contains more power in a narrow band, while the spread signal contains the same power for a sufficiently greater bandwidth with a lower peak power. This enables the spread signal to reside within or be camouflaged by the environment noise.
With respect to Direct Sequence Spread Spectrum, PN acquisition is the process of estimating the phase of a received pseudonoise code and adjusting the local code to the phase estimate to place the local and received codes substantially in phase (e.g., within one-half of a chip). If the local and received pseudonoise codes are substantially in phase, the despreading process produces a signal similar to a non-spread baseband signal (e.g., Sbb(t) in FIG. 1) with some loss in signal amplitude that is proportional to the phase difference between the local and received codes. This applies only when the received and local pseudonoise codes are substantially in phase. If the received and local pseudonoise codes are out of phase (e.g., a phase difference greater than one chip), this produces minimal or no signal amplitude, thereby preventing carrier acquisition.
When the local and received pseudonoise codes are substantially in phase after PN acquisition and include identical chip rates, carrier acquisition for Direct Sequence Spread Spectrum signals is substantially similar to carrier acquisition for non-spread signals described above (e.g., except for some additional implementation loss due to the fact that PN acquisition does not perfectly match the phases of the two codes). However, the chip rates of the local and received pseudonoise codes are generally not identical prior to PN tracking (e.g., tracking is a process that follows carrier acquisition). Therefore, the initial phase alignment (e.g., within one-half of a chip) from PN acquisition is temporary and the local and received code phases eventually drift apart due to the difference in chip rates. In other words, the difference in chip rates between the received and local pseudonoise codes imposes a “time limit” upon carrier acquisition (e.g., a maximum allowable carrier acquisition time). If this “time limit” is less than the minimum allowable carrier acquisition time (e.g., Tcar—acq of Equation 5), the local and received code phases may drift apart during that acquisition time and a condition of “large chip rate uncertainty” exists. Signal acquisition under this condition with conventional acquisition techniques is either unreliable (e.g., best case scenario) or impossible (e.g., worst case scenario).